Structural section



Filed May 16, 1925 11 65728 F. T. LLEWELLYN 1Q 3 k I mk .315 i I avwmtoz fFedenb/f L/e cue/(9n.

Jan. 31, 1928. F. .T. LLEWELLYN STRUCTURAL SECTION- Filed May 16, 1925 a Sheets-Sheet 2 Jan. 31, 1928. 1,657,628

I F. T. LLEWELLYN STRUCTURAL SECTION Filed May 16. 1925 I 5 Sheets-Sheet 5 Swvautoz Patented Jan.- 31, 1928.

UNITED STATES FREDERICK T. LLEWELLYN, 01E MONTCIIAIR, NEW JERSEY.

STRUCTURAL SECTION.

Application filed May 16, 1925. Serial No. 30,694.

The invention relates to improvements in structural members such as beams, girders, columns, rails, struts and various rolled, cast or forged metal parts and aims to providea fillet of novel form for uniting adjacent parts of such members.

'lhe invention will be understood by those skilled in the art from the'following specification when read in connection with the accompanying drawings in which Fig. 1 is a transverse sectional view of an Lbeam having its flanges joined to the web thereof by fillets embodying features of my invention.

Fig. 2 is a diagram illustrating steps to he followed in plotting a parabolic fillet which is tangent to the surfaces to be united.

Fig. 3 is a diagram illustrating advantagesof my improved fillet over one formed by a circular arc of the same spread;

Fig. 4 is a table of formulas showing the simplicity of the formulas used in calculating the properties of my improved fillet over the formulas used in calculating the properi ties of arcuate fillets.

arcuate form having the same area;

Fig. 6 is an enlarged section of an angle whose flanges are joined by a parabolic fillet and illustrates the saving in grinding the edge of a punching die used for punching holes close to the fillet.

Referring in detail to the embodiments of my invention, Fig. 1 is an exemplification in the form of an -I-beam comprising a web portion 10, having flanges l9. united thereto by my improved fillets 14 having a' particular iiorm or contour as hereinafter more fully disclosed.

It is the practice in the structural art to effect the junction between two intersecting surfaces of a section or part by means of a three-sided fillet two of whose sides coincide with extensions of the surfaces to be connected, while the third side consists of a concave curved surface which at its outer edges is tangential to the two surfaces to be joined. Hitherto the form of curve used has been a circular arc, and when the metal is disposed in this form I find the section or part to be deficient as regards strength, adaptability, regularity of contour, quality of product, ease of manufactuie, and calculability of properties.

An object of my invention is to reduce or to eliminate these deficiencies, and I achieve.

this by using a portion of a parabolic curve in place of a circular are or arcs, my parabolic curve being so disposed'as to be tangential to the two surfaces to be united. 'lhis disposition I accomplish, in the most usual case of symmetrical fillets, by making the principal axis of the parabola bisect the angle between the two planes to be united. In the rarer case of unsymmetrical fillets it is impossible to form the curved surface by means of a single circular arc, and recourse has hitherto been had to a complicated combination of two or more arcs 'of different radii the calculation of whose properties is extremely tedious. By my invention a single parabolic curve is easil adjusted to this case, as is illustrated in ig. 2 by the following method which applies whatever may be the angle between the surfaces to be united and whatever may be the lengths of the intersecting tangents Bl) and FD.

To locate a parabolic curve tangential to BD and FD.

Draw DL throu h N, the middle point of BF and draw BL W and B DF perpendicular to DL, and BB and .WFF parallel. to DL.

The intersection, C of BF and B F will be the vertex of the desired parabola, whose principal axis will be parallel to DL.

Draw BG perpendicular to BD,and make CO=% GK. Then 0 will be the focus of the parabola.

With this data the curve can be traced and the enclosed area and properties calculated from well known parabolic equations.

The reason for the greater simplicity of calculations involving my parabolic curve when combined with such tangents lies in the fact that formulas using its rectilinear co-ordinates involve the use of a first power of one ordinate and a second power of the other, whereas the circular arc formulas involve the use of second powers of both ordinates.

Such formulas are shown in the table, Fig. 4, which should be read in connection with Figs. 3 and 5. In these figures the spread of the arcuate filletsend parabolic fillets are indicated by the dimension lines T and F respectively.

The point of intersection of lines projected from the web and flanges as shown ter of gravity of the parabolic fillet from the root.

and sp equal the respective distances from the root to the fillet as measured inv a radial line in the case of the arc, and in a line passin through the focus in the case of the para ola.

The location of the center of gravity of the fillet area and other data given in igs. 3, .4 and 5 is especially useful in calculating the strength of sections having my improved form of fillet.

In Fig. 4, the first three columns apply to any equilateral tangential fillet. The last six columns apply to a specific angle of flange slope, i. e. when 41=5 degrees.

Column 1 indexes the properties required in the art Area= area of fillet.

do or dp vertical distance from center of gravity arcuate or parabolic fillet, respectively, to root.

we or wp=corresponding tance.

so or sp==minimum distance from arcuate or parabolic curve, respectivel to root.

I =moment of inertia of llet about a horizontal axis through its center of gravity.

I =corresponding moment of through a vertical axis.

Column 2 gives formulas for properties of an arcuate fillet in terms of radius (R) and half the radial angle noting from Figs.

3 and 5 that i gi where l/ angles of horizontal dis:

inertia slo e.

Column three gives corresponding formulas for a parabolic fillet in direct terms of tangential spread (F) and angle of slope #1.

Column .four translates column 2 formulas into co-etficients of the radius of an arcuate fillet when =5 degrees.

Column five expresses column 4: as coefficients of spread so as to permit direct comparison with parabolic fillet. This is accomplished by dividing. column 4 by the respective power of .9163, as' spread=Rw .9163 (Col. 4).

Column seven similarly translates column 3 formulas into co-eificients of the spread o a parabolic fillet wheii {b -*5 degrees.

Columnsix gives in percentages a comparison of columns 5 and 7 showing the advantage of a parabolic over an arcuate fillet when both have the same spread (F or T),

the most important being a saving of 20.1 per cent in area.

Column nine expresses column 4 as ooefiicien'ts of the spread of an arcuate fillet having the same area as a parabolic fillet, when =5 degrees.

Column eight gives in percentages a comparison of columns 9 and 7, showing the advanta e of a parabolic over an arcuate fillet when laoth have the same area, the most important being an increase of 11.9 per cent in spread.

As regards strength, it is a principle accepted in the structural art that the efficiency of a section or part is increased by disposing as much metal as possible as far as possible from its center of area. I give in Fig. 4 an exact table which shows in column six that with a flange slope of 5 degrees, for the same tangential spread the cross sectional area of my parabolic fillet shown in full lines in Fig. 3 is 20.1 per cent less than that of a circular arc filletshown dotted, or that with the same area offillet as shown graphically in Fig. 5 its tangential spread is 11.9 per centgreater. For a flatter slope my advantages are greater. I

transfer all, or a portion of, my saving in area of metal to the flange or flanges, where it is further from the center of area and consequently gives a stronger section or part for a given weight.

As to adaptability, it is apparent from Figs. 3 and 6 that less trimming is re uired at the end of a member that is frame into the side of a section utilizing my parabolic fillet. Another example of its greater adaptability is illustrated in Fig. 6 where it can be shown that 26 per cent less grinding is necessary aroundthe edge 16 of a punching-die 18 when holes are punched close to the fillet of a section (as is often required), and this decrease in amount of die-metal ground off (indicated by the area 20 between the full and dotted lines) corres 0ndingly increases the life of the die. nder my invention also the under side of nuts or bolt heads can fit more snugly against the surface of the flange or leg of a section utilizing my parabolic fillet.

Concerning the advantage of the regularity of contour of my fillet, it is well known in the art of rolling metal sections that in the production of certain sections, unless the fillet is given ample spread, there is a tendency for the web metal adjacent to the root to draw out thinner than elsewhere. This irregularity (which is also a source of weakness at a critical point) is decreased or elimf inated by the increased spread of fillet that I provide as explained above.

Regarding the improved quality of prodnot it is well known in the structural art that one of the desiderata in a metal section or part, whether rolled or cast, is freedom from ltlll g at intersections unbalanced internal cooling stresses, and also that such stresses are greatest when metal is massed at one portion of a section or part which consequently cools slowly, 'as compared with thinner portions which cool more rapidly. Figs. 3 and 5 show that my parabolic fillet decreases the mass of metal (which are necessarily the thickest portions) and thereby makes for more uniform cooling of the section or part during production, and hence resultsin a better quality of product.

Another advantage of my invention lies in the ease. of manufacture. N on-symmetri'- cal rolled sections using my parabolic fillet are less distorted as they'cool, and require less subsequent straightening. In the case of castings which cannot the corresponding decrease in distortion en-v ables the manufacturer to utilize partsthat otherwisehe would have to scrap.

As regards calculability of properties,.it

is well known'in the structural art that the accurate calculation of the properties of sections or parts using circular arc fillets is so cumbersome that it has been the practice of many manufacturers'to entirely disregard the effect of fillets on strength properties, despite the fact that in certain cases this practice roduces errors of nearly 6 per cent. Indeed, l believe that some of the circular arc formulasfor such calculations, which I give in Fig. 4, have never before been derived. A comparison of these formulas (in column two') with the corresponding ones for my parabolic fillet, (in column three) given in Fig. 4, shows the much greater 'tices, it is not be straightened,

simplicity properties ofall sections parabolic fillet can be easily calculated, and thereby the tradecan readily receive the benefit of exact instead of the present approximate-properties. g

Thou h the invention has been described With're erence to structural sections having fillets of given proportions and characteristo be construed that I am limited. to the examples given. The description anddrawings should be interpreted in an illustrative rather than as various modifications may be made by those skilled in the art without departing from the invention as defined in the appended claims.

What I claim is: a

1. A structural member having surfaces united by a fillet tour is a parabolic curve.

2. A structural memberhaving surfaces united by a fillet whose cross-sectional contour is a parabolic curve, the ends of which are tangent to said surfaces.

a limiting sense,

of the latter. Thus, the accurate or parts using my.

whose cross-sectional con- 3. A rolled structural memberhaving a flange and a web united by a fillet whose cross-sectional contour is a parabolic curve the 'ends of which are tangent to said flange .and said .web.

signed my name. 1

FREDERICK T. LLEWELLYN.

is a para- 

